A result on integral functionals with infinitely many constraints

Tahir Choulli (University of Alberta, Department of Mathematical and Statistical Sciences, 632 Central Academic Building, Edmonton, AB T6G 2G1, Canada), Martin Schweizer (ETH Zürich, Departement Mathematik, ETH-Zentrum, HG G 51.2, CH-8092 Zürich, Switzerland and Swiss Finance Institute, CH-8006 Zürich, Switzerland)

A classic paper of Borwein/Lewis (1991) studies optimisation problems over L^p_+ with finitely many linear equality constraints, given by scalar products with functions from L^q. One key result shows that if some x in L^p_+ satisfies the constraints and if the constraint functions are pseudo-Haar, the constraints can also be realised by another function y in the interior of L^\infty_+ . We establish an analogue of this result in a setting with infinitely many, measurably parametrised constraints, and we briefly sketch an application in arbitrage theory

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Year of publication:	14.09.2015 ; This version: 14.09.2015
Authors:	Choulli, Tahir ; Schweizer, Martin
Publisher:	Geneva : Swiss Finance Institute
Subject:	linear equality constraints \| feasible solution \| infinitely many constraints \| random measure \| arbitrage theory \| equivalent martingale measures \| Theorie \| Theory \| Martingal \| Martingale \| Unvollkommener Markt \| Incomplete market

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